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the beginning of which Jupiter enters the sign Mēsha because at that moment he also enters the nakshatra Aśvinī, and so on. (For the correspondence of nakshatras and signs see Table XXII.) We have to learn how these twelve-year cycle names conform to those of the sixty-year cycle, and also to know how to find the position of Jupiter amongst the nakshatras and signs. His position is calculated sometimes by his mean motion, sometimes by his apparent motion. The habit of the people who used this system—notably the people of Malabar and Tinnevelly—was to specify the sign in which Jupiter stood at a particular time. Suppose an inscription to state that Jupiter was in Mēsha at the time recorded. Since there are five cycles of twelve saṁvatsaras in one cycle of sixty saṁvatsaras, the fact that Jupiter was in Mēsha means that he was either in (see Table XXXII.) 3 Śukla, or 15 Vṛisha, or 27 Vijaya, or 49 Viśvāvasu, or 51 Piṅgala.
176. The easiest way to find which of the five possible sixty-year cycle saṁvatsaras corresponds to a given twelve-sign cycle saṁvatsara is to refer to Table I. If, for instance, an inscription gives the date as in the Kollam year 427 with Jupiter in Mēsha,[1] we refer to Table I. and find that Kollam 427–428 corresponds to the northern sixty-year cycle No. 51 Piṅgala; and reference to Table XXXII. shows that Piṅgala was a year in which, by his mean longitude, Jupiter stood in Mēsha.
Another way is to subtract from the number of the given year, converted to A.D. reckoning or to that of the Kaliyuga, the number of the year, by either of the latter, in which the first of the sixty-year cycle, Prabhava, began, as given in Tables XXVII., XXVIII., XXIX., XXX. or XXXI., according to the different authorities. The given year was Kollam 427. As this begins in the month Simha or Kanya the Mésha with which we are concerned is that of K.Y. 4354 expired, or A.D. 1253. No. 1 Prabhava of the sixty-year cycle began, by all the authorities noted in my Tables, in K.Y. 4303, or A.D. 1202. 4354 − 4303, or 1253 − 1202 = 51. No. 51 is Piṅgala, and by col. 3, Table XXXII., Jupiter was, during Pingala, in Mésha.
177. Table XXXII. shows the correspondence of the sixty-year cycle names with the position of Jupiter, calculated by his mean motion, in the twelve signs. The Table is applicable to both Northern and Southern India down to closely about A.D. 909, and after that date to Northern India only. The saṁvatsaras both of the twelve-year sign system (cols. 2, 3, Table XXXII.) and of the sixty-saṁvatsara cycle are similar in length and begin at the same moment.
178. For special purposes we often want to know more than the correspondence of these names and signs. We may want to know Jupiter's longitudinal position amongst the signs on a particular day or hour (A) with reference to his mean, or (B) to his apparent longitude; or (C) the same with reference to the nakshatras. These are dealt with in the following sections.
179. In the "Additions and Corrections" to the Indian Calendar, pp. 155–161, we published a set of Tables with instructions for use, showing how to find both the mean and true longitudes, in other words the mean place and the true place, of Jupiter for any year, day and time, in ghaṭikās and palas. I now republish these in somewhat different form.
In the first place I have altered Table W., "For finding the mean place of Jupiter," by giving the constant at the heading not as from Śaka 1 current, but as from the epoch of the Kaliyuga. This enables us to obtain the mean place of Jupiter for the beginning of any year from 3102 B.C., instead of being able to begin only from Śaka 1 current or A.D. 78. It also simplifies work by eliminating the necessity for using any set of figures as constants for some of the Siddhāntas. That this course yields precisely the same results as does Table W is easily proved. I work by my new Table for the beginning
- ↑ As in Kielhorn's No. 2 in Indian Antiquary, Vol. XXV. (1896), p. 54.